Log по основанию 6 (х+11)=log по основанию 7 (х+11)

Решите задачу:

$\displaystyle \log_6(x+11)=\log_7(x+11);$

$\displaystyle \frac{\log(x+11)}{\log(6)}=\frac{\log(x+11)}{\log(7)};$

$\displaystyle \log(x+11)\log(7)=\log(x+11)\log(6);$

$\displaystyle \log(x+11)\log(7)-\log(x+11)\log(6)=0;$

$\displaystyle \log(x+11)\left(\log(7)-\log(6)\right)=0;$

$\displaystyle \log(x+11)=0;$

$\displaystyle x+11=1;$

$\displaystyle \therefore{x=\boxed{-10}\phantom{.}}.$